The need for better performance of turbomachinery with active magnetic bearings has necessitated a study of such systems for accurate prediction of their vibrational characteristics. This research presents a modification of existing transfer matrix methods for rotor analysis, to predict the response of rotor systems with active magnetic bearings. The position of the magnetic bearing sensors is taken into account and the effect of changing sensor position on the vibrational characteristics of rotor systems is studied. The modified algorithm is validated using a simpler modified Jeffcott model. The effect of changing from a rotating unbalance excitation to a constant excitation in a single plane is also studied. An eight-stage centrifugal compressor rotor is analyzed using the modified transfer matrix code. The results for a two-mass Jeffcott model are presented as plots of critical frequency vs. sensor position and amplitude at critical frequency vs. sensor position. Plots of amplitude vs. frequency and phase angle vs. frequency for different cases of sensor location are also presented. The results obtained by analyzing this two-mass model with the modified transfer matrix method have been compared with the results of the modified Jeffcott analysis for the purpose of verification. Also included are plots of amplitude vs. frequency and phase angle vs. frequency for the eight-stage centrifugal compressor rotor. These plots will demonstrate the significant influence that sensor location has on the critical frequencies and the amplitudes at the critical frequencies of the rotor system. / Master of Science